Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
A school in one country has $400$ students. Every student was asked if they preferred swimming, cycling or running, and the outcomes are shown in the table below. One student is selected at random.
(a(i))[1]
Find the probability that the chosen student prefers swimming.
(a(ii))[2]
Determine whether the events ‘the student is male’ and ‘the student prefers swimming’ are independent, and justify your answer.
(b(i))[3]
A random sample of 10 students from this country is selected. Find the probability that at least 3 of these students do not like any sports.
(b(ii))[5]
A random sample of 90 students from this country is now chosen. Use an approximation to find the probability that fewer than 32 of them do not like any sports.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate evaluation $\frac{104+31}{400}=\frac{135}{400}=\frac{27}{80}$” …